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Equation 14 · Part 5 · The Real Economics of Shipping a Model to a Device

Symbol Q

TCdevice=Cdev+U+Q⋅cd,TCcloud=Q⋅ccloud,TC_{\mathrm{device}} = C_{\mathrm{dev}} + U + Q \cdot c_{d}, \qquad TC_{\mathrm{cloud}} = Q \cdot c_{\mathrm{cloud}},
QQ

What this part means

Q is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

Q is one of the signed contributions combined to compute the quantity on the left.

The passage around this formula

…in the next section. Define cdc_{d} as the marginal cost of one additional on-device inference and ccloudc_{\mathrm{cloud}} as the marginal cost of one additional cloud-served inference of the same model. Total cost over Q queries under each placement is TCdevice=Cdev+U+Q⋅cd,TCcloud=Q⋅ccloudTC_{\mathrm{device}} = C_{\mathrm{dev}} + U + Q \cdot c_{d}, \qquad TC_{\mathrm{cloud}} = Q \cdot c_{\mathrm{cloud}}. and the break-even query volume — the point at which on-device placement stops costing more than cloud placement — is

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A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

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